William W. -G. Yeh

We present a multi‐objective, multi‐stage stochastic programming with recourse model for reservoir management and operation, where we use utility theory to select the best compromise solution from the Pareto front. A multi‐stage streamflow scenario tree is generated first by the neural gas method. Then the Pareto front at each stage is produced by a modified constrained NSGA‐II. A single best compromise solution on the Pareto front must be selected for the immediate stage and the model moves forward one stage and is re‐optimized over a moving planning horizon of fixed duration. A key contribution of this study is the selection of the best compromise solution, which is achieved by a proposed linear spline utility function allied with regression. Our proposed utility function has the following advantages: (a) It satisfies the law of diminishing marginal rate of substitution, (b) it does not rely on the pre‐specified weight or goal, and (c) it selects the best compromise solution that is likely to fall in the “knee regions” of the Pareto front. We apply the proposed optimization model to the Three Gorges Reservoir in China. The two conflicting objectives are (a) maximizing the total expected energy output in the planning horizon, and (b) maximizing the average expected ecological benefits in the planning horizon. The results show that the proposed model produces the optimal water release policy successfully under different hydrological scenarios, considering both the inflow uncertainty and the tradeoff between the two conflicting objectives.

In data‐scarce regions, seasonal hydropower planning is hindered by the unavailability of reliable long‐term streamflow observations, which are required for the construction of inflow scenario trees. In this study, we develop a methodological framework to overcome the problem of streamflow data scarcity by combining precipitation forecasts from ensemble numerical weather prediction models, spatially distributed hydrologic models, and stochastic programming. We use evapotranspiration as a proxy for streamflow in generating reliable reservoir inflow forecasts. Using the framework, we compare three different formulations of inflow scenario structures and their applicability to data‐scarce regions: (1) a single deterministic forecast, (2) a scenario fan with the first stage deterministic, and (3) a scenario fan with all stages stochastic. We apply the framework to a cascade of two reservoirs in the Omo‐Gibe River basin in Ethiopia. Future reservoir inflows are generated using a 3‐model 30‐member ensemble seasonal precipitation forecast from the North American Multimodel Ensemble and the Noah‐MP hydrologic model. We then perform deterministic and stochastic optimization for hydropower operation and planning. Comparing the results from the three different inflow scenario structures, we observe that the uncertainty in reservoir inflows is significant only for the dry stages of the planning horizon. In addition, we find that the impact of model parameter uncertainty on hydropower production is significant (0.14–0.18×10⁶ MWh).

The Brazilian interconnected hydropower system consists of a linked network of 151 medium and large reservoirs, and is complemented by a large set of small hydropower, thermal, and wind power plants, with a total installed capacity of 162 GW. Energy, flood control, public water supply, irrigation, animal raising, wastewater disposal, navigation, and environment protection are among the multiple water uses of the system. In Brazil, hydropower is the predominant source of energy supply, representing from 71% to 93% of total energy consumption in the country during the last 17 years. The reservoir storage in the multi-reservoir system varies from 286,174 mm³ to 573,600 mm³, and the forebay area varies from 22,715 km² to 37,894 km². Installed energy production and storage capacities, and hydrological conditions vary significantly among different regions in the country. Evaporation losses from the storage reservoir are significant and must be accurately estimated. In this paper we use the HIDROTERM, a nonlinear programming optimization model previously developed for planning the operation of the Brazilian hydrothermal system, to estimate the loss of energy production in the system due to evaporation loss. We use different hydrological scenarios and different initial conditions to study the impact of energy loss among different reservoirs and regions in the country. The study is important for planning purposes, especially when the system is undergoing severe droughts.

This paper proposes a practical procedure for optimizing the daily operation of a large‐scale hydrothermal system. The overall procedure optimizes a monthly model over a period of 1 year and a daily model over a period of up to 1 month. The outputs from the monthly model are used as inputs and boundary conditions for the daily model. The models iterate and update when new information becomes available. The monthly hydrothermal model uses nonlinear programing (NLP) to minimize fuel costs, while maximizing hydropower production. The daily model consists of a hydro model, a thermal model, and a combined hydrothermal model. The hydro model and thermal model generate the initial feasible solutions for the hydrothermal model. The two competing objectives considered in the daily hydrothermal model are minimizing fuel costs and minimizing thermal emissions. We use the constraint method to develop the trade‐off curve (Pareto front) between these two objectives. We apply the proposed methodology on the Yunnan hydrothermal system in China. The system consists of 163 individual hydropower plants with an installed capacity of 48,477 MW and 11 individual thermal plants with an installed capacity of 12,400 MW. We use historical operational records to verify the correctness of the model and to test the robustness of the methodology. The results demonstrate the practicability and validity of the proposed procedure.

Multiple uncertainties exist in the optimal flood control decision‐making process, presenting risks involving flood control decisions. This paper defines the main steps in optimal flood control decision making that constitute the Forecast‐Optimization‐Decision Making (FODM) chain. We propose a framework for supporting optimal flood control decision making under multiple uncertainties and evaluate risk propagation along the FODM chain from a holistic perspective. To deal with uncertainties, we employ stochastic models at each link of the FODM chain. We generate synthetic ensemble flood forecasts via the martingale model of forecast evolution. We then establish a multiobjective stochastic programming with recourse model for optimal flood control operation. The Pareto front under uncertainty is derived via the constraint method coupled with a two‐step process. We propose a novel SMAA‐TOPSIS model for stochastic multicriteria decision making. Then we propose the risk assessment model, the risk of decision‐making errors and rank uncertainty degree to quantify the risk propagation process along the FODM chain. We conduct numerical experiments to investigate the effects of flood forecast uncertainty on optimal flood control decision making and risk propagation. We apply the proposed methodology to a flood control system in the Daduhe River basin in China. The results indicate that the proposed method can provide valuable risk information in each link of the FODM chain and enable risk‐informed decisions with higher reliability.

The Paraíba do Sul River Basin is an important basin located between the largest industrial region and densely populated cities in Brazil. The basin includes parts of the states of São Paulo, Rio de Janeiro and Minas Gerais. Main water uses include public supply, irrigation, wastewater disposal and hydropower production. Five storage reservoirs with hydropower plants are used to regulate inflows and produce hydropower. To comply with water supply security and environmental protection requirements, additional operational constraints on storage levels and releases are being imposed. The 12 million inhabitants in the Rio de Janeiro metropolitan region receive their main water supply from the reservoir system. To improve water supply safety after the severe drought of 2012-2015, a new water transfer project is being built in the São Paulo metropolitan region that has 20 million inhabitants. The 2012-2015 drought affected several basins in Brazil and required reduction in minimum release constraints on the reservoirs of the Paraíba do Sul River Basin. Moreover, construction of the new water transfer project requires a temporary reduction of the maximum storage levels. In this paper we use the HIDROTERM, a nonlinear programming optimization model previously developed for planning the operation of the Brazilian hydrothermal system, to evaluate the impact of the additional constraints and changes that are imposed on the reservoir system. Specifically, we use different hydrological scenarios to evaluate the impact on hydropower production and other water uses as well as the risk of not meeting the constraints.

The Brazilian interconnected power system consists of 153 medium and large hydropower plants, and is complemented by a large set of small hydropower, thermal and wind power plants. Hydropower is the predominant source of energy supply and on average represents 85% of total energy consumption in the country during the last ten years. Inflow forecasts are required for the planning and operation of the power system. The current practice is to utilize a set of streamflow forecasting models to predict reservoir inflows, which are used as inputs to the optimization models. The purpose of the study is to evaluate the accuracy of the forecasting models that are being used by the electric system national operator (ONS). We use statistical analysis by comparing the forecasts with historical observations at various reservoir sites and different seasons. Short-term forecasts are important for real-time operation, mainly for flood control and unit commitment. For monthly planning and operation, the hydro system optimization model uses deterministic reservoir inflow forecasts for the first month and different scenarios to represent future possible inflows after the first month until the end of the planning horizon. The optimization model is solved by stochastic programming with recourse and is updated at the beginning of each month. This paper evaluates the accuracy of monthly inflow forecasts for all the medium and large hydropower plants in Brazil. We intend to answer the following questions. How is the goodness of fit among different periods and river basins? How can the forecasting models be improved?

Risk analysis plays an important role in decision making for real‐time flood control operation of complex flood control systems. A typical flood control system consists of reservoirs, river channels, and downstream control points. The system generally is characterized by nonlinearity and large scale. Additionally, the input variables are mostly stochastic. Because of the dimensionality problem, generally, it would not be possible to carry out risk analysis without decomposition. In this paper, we propose a decomposition‐integration approach whereby the original complex flood control system is decomposed into a number of independent subsystems. We conduct risk analysis for each subsystem and then integrate the results by means of combination theory of stochastic processes. We evaluate the propagation of uncertainties through the complex flood control system and calculate the risk of reservoir overtopping, as well as the risk of flooding at selected downstream control points. We apply the proposed methodology to a flood control system in the middle reaches of the Huaihe River basin in China. The results show that the proposed method is practical and provides a way to estimate the risks in real‐time flood control operation of a complex flood control system.

The Brazilian interconnected power system consists of a set of over 150 medium and large hydropower plants, and is complemented by a large set of small hydropower plants, and thermal and wind power plants. Hydropower plants are operated to meet most of the energy demand, while the complementary system is dispatched to make up the shortage in supply. During 13 years from 2000 to 2012 on average 91% of Brazilian effective electric generation was provided by hydropower. However, in the last three years this percentage was reduced, in sequence, to 79, 73, and 71%. Intense and expensive thermal dispatch was necessary, while hydropower production was reduced and reservoir storages were drawn down. In the last three years, several major watersheds in Brazil have experienced a very severe drought. At the same time, the energy problem was exacerbated by demand increase and delayed expansion of the power system. To analyze the impacts of drought on the hydropower system, we propose to focus not only on the inflows but also on energy. Three variables were compared: historical reservoir inflows from 1930 to 2015, corresponding energy inflows, and optimal hydropower production. A nonlinear programming model, called HIDROTERM, previously developed for the hydrothermal system, was used to evaluate the optimal hydropower production under the historical inflows. We analyzed the intensity and duration of the historical droughts and evaluated the impacts of the most recent 2012–2015 severe drought on the Brazilian hydropower system.